Author(s)

P. S. Farrugia & A. Micallef

Abstract

Wind is a 3D vector quantity. However, it is frequently found that the vertical component is much smaller in magnitude than the horizontal ones and acts over shorter distances so that its effect is considered negligible. As a result of this, wind is often treated as a two dimensional circular variable. In fact, most of the statistical treatment used to derive the wind angular dispersion, a parameter that is very important in determining the rate of diffusion of pollutants, is based on this assumption. Nevertheless, the reduction of a dimension might not always be justified. A case in point occurs when considering air flow in a street canyon whereby all three directions of air flow can be significant. In such a situation, a 3D measure of angular dispersion would be much more appropriate. For this reason, this work concentrates on establishing consistent 3D measures of angular dispersion. Thus a detailed geometric analysis of an existing and widely used measure of 3D angular dispersion was carried out. This showed that this measure accounts for dispersion mainly along one direction. In order to improve on this, a new set of measures for angular dispersion that account for all three directions is derived using some recently proposed measures of angular dispersion. It is also shown that these new measures can be further extended to any dimension. Keywords: spherical variables, three dimensional measure of angular dispersion, spherical variance, projection variance, geometric variance, diffusion of pollutants in three dimensions, angular dispersion in any dimension. 1 Introduction Air motion, can occur in any of the three spatial dimensions. However, it is common practice to ignore the vertical component since this is frequently much

Keywords

spherical variables, three dimensional measure of angular dispersion, spherical variance, projection variance, geometric variance, diffusion of pollutants in three dimensions, angular dispersion in any dimension.